Classical molecular dynamics simulations have been carried out for lanthanide ions Ln(3+) in aqueous solution. For the Ln(3+)-water interaction we propose a new three-body potential function that takes into account the mean polarization of water molecules in the first hydration shell and that has been fitted to ab-initio results. By a usual pair potential approach we can reproduce the experimental distance of the first maximum in the cation-oxygen radial pair distribution function, but the first hydration shell is by far too unstable from both a structural and a dynamical point of view. Inclusion of a polarization term leads to a perfect agreement with coordination numbers from neutron diffraction studies as well as to decreased kinetic lability of the first hydration shell that is more consistent with experimental evidence. Notably, a coordination number of 8.5 is obtained for the middle of the lanthanide series and corresponds to an equilibrium between a 9-coordinated and an 8-coordinated Ln(3+)-aqua ion. Water exchange rate constants from computer simulations are reported for the first time for Ln(3+)-aqua ions. A maximum of the exchange rate constants in the middle of the series is in agreement with the current interpretation of experimental data, based on the change of relative stability of the ennea and octa aqua ions along the series.